I calculated the phase shifts that the sidebands would pick up in the arms in the case we changed the arm length to 38.4m as proposed. I obtained the following values (in degrees):
phi(-f2) = 0.66; phi(-f1) = -0.71; phi(f1) = 0.71; phi(+f2) = -0.66
These are the plots with the results as I obtained from an Optickle simulation (the second zooms in around 38.4m).
These values agree with what Koji had already estimated (see elog entry 3023).
Since we can't make the arm longer than that, to increase the distance from the resonance, we would like to adjust the length of the short cavities to compensate for that. For f2 (=55MHz), 0.7 degrees correspond to about 5cm. That is about the length change that we expect to make to the design.
I simulated with Optickle the effect of changing the length of either the SRC or the PRC. The best way I found to do that, was to measure the cavity circulating power when the macroscopic lengths change.
The following plots show the effect of changing either the PRC or SRC length (left or right figure), on the circulating power of both cavities at the same time (top and bottom plots).
You can compare these with the case of perfect antiresonance as in the following plots:
It seems that the design length for the short cavities are not too bad. f1 is not optimized in the PRC, but changing the length of the cavity wold just make f2 worse in SRC.
These simulations seem to support the choice of not changing the design cavity lengths for PRC and SRC.
Of course these are only an "open loop" simulations. At the moment we don't know what would be the effect of closing the control loops. That is something I'm going to do later. It'll be part of my studies on the effects of cavity absolute length on the whole IFO.